The equivalence of convex and concave transport cost in a circular spatial model with and without zoning

This article depicts a location game in a circular market. The equivalence results between a convex and a concave transport cost are reexamined by assuming an arbitrary length. In contrast to previous research the solution found shows that the equivalence relationship depends on the space length. Furthermore, the analysis is extended to a circular model with unitary length and zoning. In this case equivalence does not hold. Moreover, non-existence of equilibrium is shown under strictly linear quadratic functions. Surprisingly, equilibrium exists for a concave quadratic function but not for a convex quadratic function.